Christmann studied oriental subjects at Heidelberg and
became a teacher there in 1580. Shortly thereafter,
however, he had to leave that university because he, as a
Calvinist, could not subscribe to the concordat-formulary
set down by the Lutheran Elector Ludwig VI. Christmann
traveled for some time, then settled down to teach in a
Reformed school in Neustadt, Pfalz. He was a teacher
there in 1582. The death of Ludwig (12 October 1583)
enabled him to return to Heidelberg, where he was
appointed professor of Hebrew on 18 June 1584. From
1591 on he taught Aristotelian logic. He was made reetor
of the university in 1602.

In 1608 Frederick IV appointed Christmann professor
of Arabic. Christmann thus became the second teacher
of that subject in Europe, the first having been Guillaume
Postel at Paris in 1538. This appointment must have given
great satisfaction to its recipient, since in 1590, in the
preface of his Alfragani chronologica et astronomica
elementa, Christmann had advocated the establishment of
a chair of Arabic "to open possibilities for teaching
philosophy and medicine from the [original] sources".
Indeed, Christmann had demonstrated his scholarly
interest in the Arabic language as early as 1582, with the
publication of his Alphabeticum Arabicum, a small book of
rules for reading and writing Arabic. Besides Arabic, he
is said to have known Syrian, Chaldaic, Greek, Latin,
French, Italian, and Spanish. He was an extremely modest
man despite his learning, with a passion for work that
may well have hastened his death of jaundice.

On the death of Valentine Otho, Cbristmann inherited
the entire library of G. J. Rhäticus, which had been in
Otho's keeping. This collection contained trigonometric
tables more extensive than those that Rhäticus had
published in the Opus Palatinum of 1596 (adapted by B.
Pitiscus as the basis for his Thesaurus mathematicus of
1613) as well as the original manuscript of Copernicus'
De revolutionibus orbium coelestium. The inclusion of
instruments in the bequest stimulated Christmann to
begin making astronomical observations. In 1604 he
proposed to Kepler that they should exchange the results
of their researches. Christmann was the first to use the
telescope in conjunction with such instruments as the
sextant or Jacob's staff (1611), with the results reported in
his Theoria lunae and Nodus gordius. These last works also
show him to be a competent astronomical theorist. He
gave a good treatment of prosthaphaeresis, the best
method of calculating trigonometric tables
to be developed before the invention of logarithms, which
he based on such formulas as
2 sin A sin B = cos (A - B) - cos (A + B);
he then went on to prove that this method had been
devised by Johann Werner.

In his Tractatio geometrica de quadratura circuli,
Christmann defended against J. J. Scaliger the thesis that
the quadrature of the circle could be solved only
approximately. In his books on chronology - a topic of
great concern at a time of radical calendar reform - he
disputed the work of not only Scaliger but also J. J.
Lipsius. He further criticized Copernicus, Tycho Brahe,
and Clavius - some such criticisms may be found in some
detail in manuscript annotations of his own copy
of Alfragani chronologica et astronomica elementa, which is
now in the library of the University of Utrecht.